Mathematics of Molecular and Cellular Biology

Doug Arnold, the director of IMA, has been elected as the new president of SIAM. His 2-year term will begin in January, 2009.

Math video -- the top featured video on youtube

Möbius Transformations Revealed, a short video by IMA director Douglas
Arnold and colleague Jonathan Rogness, which depicts the beauty of Möbius transformations and
shows how moving to a higher dimension reveals their essential unity, is currently the top featured video on www.youtube.com and has been watched by almost 1000,000 viewers. -- so for a brief shining moment, at least, stereographic projection and Möbius Transformations are getting top billing over talking cats and charging an iPod with gatorade. It can be found at www.ima.umn.edu/~arnold/moebius/
.

Application deadlines: If you are interested in applying for one of the IMA "New Directions Research Professorship" or "Postdoctoral Fellowship" positions in connection with the 2008-2009 thematic program: Mathematics and Chemistry, the deadline for applying for the postdoc positions is January 5, 2008 and the deadline for the New Directions Research Professorships is January 15, 2008. You can find the applications for these positions at our Applications site.

Monday, December 31

Event Legend:

Using mathematical modeling to make testable predictions of cellular signaling pathways

Abstract: We propose a mathematical model of the G-protein signaling pathway in RAW 264.7 macrophages downstream of P2Y6 activation by the ubiquitous signaling nucleotide uridine 5-diphosphate. The model is based on time-course measurements of P2Y6 surface receptors, inositol trisphosphate, cytosolic calcium, and with a particular focus on differential dynamics of multiple species of diacylglycerol. When using the canonical representation, the model predicted that key interactions were missing from the current pathway structure. Indeed, the model suggested that to accurately depict experimental observations, an additional branch to the signaling pathway was needed, whereby an intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

Abstract: Difference topology is a methodology to derive the number of DNA crossings trapped in an unknown protein complex. By this method, Pathania, Jayaram, and Harshey revealed the topological structure within the Mu protein complex which consisted of three DNA segments containing five nodes [1]. In their experiments, they used a member of the site-specific recombinases which is known as Cre. Cre mediates DNA exchange by rearranging target sites of the DNA segments. During this DNA recombination, there are no extra DNA crossings introduced. The initial DNA conformation is unknotted. After Cre recombination, the products are knots or catenanes. Recently, Darcy, Luecke, and Vazquez analyzed these experimental results and proved that the five-noded conformation is the only biologically reasonable structure of the Mu protein DNA complex [2]. We address the possibility of protein complexes that binds four DNA segments. By the useful property of Cre, we can make the assumption that after Cre recombination, the topology of a DNA-protein complex would be a knot or catenane. The latest results of the topological tangle model for this case and very basic biological and mathematical backgrounds will be discussed.

Abstract: After a genome is replicated, it must be properly segregated into the two daughter cells. A segregation machine, known as the mitotic spindle, moves sister chromosomes into proper position for their eventual parting. This machine is composed of linear polymers known as microtubules, which dynamically self-assemble via an energy-dissipating process known as "dynamic instability". I will discuss our Monte Carlo modeling of microtubule dynamics during mitosis as it occurs in the budding yeast. Through experimental testing of our models we found that molecular motors play a key role in regulating microtubule dynamics to properly sort chromosomes during yeast mitosis.

Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures

Abstract: Recent improvements in fluorescence microscopy and digital image processing enable direct observations of thermal fluctuations in phase separating binary mixtures. For example, the analysis of capillary wave statics and dynamics in suspended mixed lipid monolayer membranes is being used to gain insight into the nature of the intermolecular interactions. Due to the level of complexity in these systems, mesoscale simulations which incorporate thermal fluctuations can significantly improve our understanding of these systems. Here we describe a recently introduced particle-based model for the fluid dynamics of immiscible binary mixtures. Excluded volume interactions between the two components are modeled by stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally, and entropically driven phase separation occurs for high collision rates. An explicit expression for the equation of state is derived. Analytic results for the phase diagram are in excellent agreement with simulation data. Results for the line tension obtained from the analysis of the capillary wave spectrum of a droplet agree with measurements based on the Laplace's equation. The dispersion relation for the capillary waves is derived and compared with the numerical measurements of the time correlations of the radial fluctuations in the damped and over-damped limits. The introduction of ``amphiphilic'' dimers makes it possible to model the phase behavior of ternary surfactant mixtures.

The solution of the boundary-value problems for the simulation of transitions of protein conformations

Abstract: Under certain kinetic or thermodynamic conditions, proteins make conformational transitions, resulting in significant functional variations. Such dynamic properties can be studied through molecular dynamics simulation. However, in contrast to conventional dynamics simulation protocols where an initial-value problem is solved, the simulation of transitions of protein conformations can be done by solving a boundary-value problem, with the beginning and ending states of the protein as the boundary conditions. While a boundary-value problem is more difficult to solve in general, it provides a more realistic model for the study of protein conformational transitions and has certain computational advantages as well, especially for large scale simulations. Here we study the solution of the boundary-value problems for the simulation of transitions of protein conformations using a standard class of numerical methods called the multiple shooting methods. We describe the methods and discuss the issues related to their implementations for our specific applications, including the definition of the boundary conditions, the formation of the initial trajectories, and the convergence of the solutions. We present the results from using the multiple shooting methods for the study of conformational transitions of a small molecular cluster and an alanine dipeptide, and show the potential extension of the methods to larger biomolecular systems.

Visitors in Residence

Douglas N. Arnold

University of Minnesota

7/15/2001 - 6/30/2008

Donald G. Aronson

University of Minnesota

9/1/2007 - 8/31/2009

F. Javier Arsuaga

San Francisco State University

9/3/2007 - 12/31/2007

Daniel J. Bates

University of Minnesota

9/1/2006 - 8/31/2008

Peter W. Bates

Michigan State University

9/1/2007 - 12/22/2007

John Baxter

University of Minnesota

8/1/2007 - 7/30/2009

Yermal Sujeet Bhat

University of Minnesota

9/1/2006 - 8/31/2008

Hannah Callender

University of Minnesota

9/1/2007 - 8/31/2009

Ludovica Cecilia Cotta-Ramusino

University of Minnesota

10/1/2007 - 8/30/2009

Isabel K. Darcy

University of Iowa

9/1/2007 - 1/19/2008

Olivier Dubois

University of Minnesota

9/3/2007 - 8/31/2009

Jason E. Gower

University of Minnesota

9/1/2006 - 8/31/2008

Milena Hering

University of Minnesota

9/1/2006 - 8/31/2008

Peter Hinow

University of Minnesota

9/1/2007 - 8/31/2009

Richard D. James

University of Minnesota

9/4/2007 - 6/30/2008

Tiefeng Jiang

University of Minnesota

9/1/2007 - 6/30/2008

Markus Keel

University of Minnesota

12/7/2007 - 12/7/2007

Soojeong Kim

University of Iowa

8/30/2007 - 1/20/2008

Debra Knisley

East Tennessee State University

8/17/2007 - 6/1/2008

Attila Gyula Kocsis

Budapest University of Technology and Economics

12/1/2007 - 12/31/2007

Chang Hyeong Lee

Worcester Polytechnic Institute

10/14/2007 - 1/4/2008

Anton Leykin

University of Minnesota

8/16/2006 - 8/15/2008

Roger Lui

Worcester Polytechnic Institute

9/1/2007 - 6/30/2008

Laura Lurati

University of Minnesota

9/1/2006 - 8/31/2008

Ezra Miller

University of Minnesota

9/1/2007 - 6/30/2008

Maria Giovanna Mora

International School for Advanced Studies (SISSA/ISAS)

9/1/2007 - 12/31/2007

Timothy Newman

Arizona State University

9/1/2007 - 6/30/2008

Duane Nykamp

University of Minnesota

9/1/2007 - 6/30/2008

David Odde

University of Minnesota

12/11/2007 - 12/11/2007

Hans G. Othmer

University of Minnesota

9/1/2007 - 6/30/2008

Deena Schmidt

University of Minnesota

9/1/2007 - 8/31/2009

Chehrzad Shakiban

University of Minnesota

9/1/2006 - 8/31/2008

Andrew Stein

University of Minnesota

9/1/2007 - 8/31/2009

Vladimir Sverak

University of Minnesota

9/1/2007 - 6/30/2008

David Swigon

University of Pittsburgh

9/4/2007 - 12/14/2007

Erkan Tüzel

University of Minnesota

9/1/2007 - 8/31/2009

Mariel Vazquez

San Francisco State University

9/3/2007 - 12/31/2007

Zhian Wang

University of Minnesota

9/1/2007 - 8/31/2009

Zhijun Wu

Iowa State University

9/4/2007 - 6/1/2008

Arghir Dani Zarnescu

University of Oxford

11/12/2007 - 12/9/2007

Hongchao Zhang

University of Minnesota

9/1/2006 - 8/31/2008

Legend:Postdoc or Industrial PostdocLong-term Visitor

IMA Affiliates:

3M, Arizona State University, Boeing, Carnegie Mellon University, Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Schlumberger-Doll Research, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute